Square Root of 888

√888 at a glance

Exact value

2√222

Decimal (10 places)

29.7993288515

Rounded

29.8 · 29.80 · 29.799

Perfect square?

No — between 29² and 30²

Rational?

Irrational

Both square roots

±29.799329

Prime factorization

2³ × 3 × 37

Cube root

9.611791

How to simplify √888

Look for the largest perfect square that divides 888. Here it is 4 (2²), because 888 = 4 × 222 and 222 has no square factor left:

The prime factorization tells the same story: 888 = 2³ × 3 × 37. Each pair of equal primes leaves the radical as one factor, so 2 comes out and 2 × 3 × 37 stays inside.

Check: (2√222)² = 2² × 222 = 4 × 222 = 888. As a decimal, 2√222 = 2 × 14.8996644258 ≈ 29.7993288515.

Where √888 sits between perfect squares

841 = 29² and 900 = 30² are the nearest perfect squares, so √888 lies between 29 and 30. 888 is 47 above 841 and 12 below 900, so the root is closer to 30.

• Straight line between 841 and 900: 29.7966 (0.01% low)
• Tangent from 29, i.e. 29 + 47 ÷ 58: 29.8103 (0.04% high)
• Tangent from 30, i.e. 30 − 12 ÷ 60: 29.8000 (0% high)

For √888 the tangent at 30 wins, missing by only 0.0007. Tangent estimates shine when the number sits close to a perfect square — here 888 is just 12 below 900.

Finding √888 with the Babylonian method

Picture a rectangle with an area of 888 and one side x; the other side must be 888 ÷ x. Averaging the two sides gives a rectangle that is closer to a square, and the side of that square is exactly √888.

Start from the nearest whole number, 30 (30² = 900):

The count of correct decimals went 3, 8 and all 10 over 3 steps — roughly doubling each time — until the guess matched √888 = 29.7993288515 to every decimal shown.

√888 as a continued fraction

Every irrational square root has a continued fraction that repeats. For √888 the pattern is [29; 1, 3, 1, 58] with the block of 4 terms after the semicolon repeating forever. A pattern that never ends is one more proof that √888 is irrational.

Cutting the continued fraction off early gives the best fractions for approximating the root — no fraction with a smaller denominator comes closer:

The same fractions solve Pell’s equation, x² − 888y² = 1. Its smallest solution in positive whole numbers is x = 149, y = 5.

√888 in geometry and everyday measurements

• 888 square feet is 82.5 m². Laid out as a square — a small house footprint or a lot — it is about 29.8 ft (29 ft 10 in) on a side.
• 888 is not a sum of two whole-number squares — the prime factor 3 (one less than a multiple of 4) appears an odd number of times, which rules that out — so √888 is never the diagonal of a rectangle with whole-number sides. It is, however, the space diagonal of a 2 × 10 × 28 box, because 2² + 10² + 28² = 888.
• Since √888 = 2√222, a length of √888 is exactly 2 copies of the length √222 laid end to end.

Square roots near √888 and related roots

• The cube root of 888 is about 9.611791.
• Because 888 = 4 × 222, the root is twice √222: 2 × 14.899664 ≈ 29.799329.

Need a different value? Use the Square root calculator, or browse the Square roots 1–1,000.